so i remember, logarith is dependence between a to c in a^b = c

so if we have 5 ^ 3 = 125 between 125 and 5 is dependence 125 / 5 = 25, so squart from 2 = 25

Definitions:

 

Natural log: y = e^x, ln(y) = x

 

Common log: y = 10^x, log(y) = x

so i remember, logarith is dependence between a to c in a^b = c

so if we have 5 ^ 3 = 125 between 125 and 5 is dependence 125 / 5 = 25, so squart from 2 = 25

 

And your second statement follows from the rule that x^3=(x^2).x - logs dont enter into it

log₁₀ ( 10 ) = 1, because 10^1=10

log₁₀ ( 100 ) = 2, because 10^2=100

log₁₀ ( 1000 ) = 3, because 10^3=1000

etc.

 

log₂ ( 2 ) = 1, because 2^1=2

log₂ ( 16 ) = 4, because 2^4=16

log₂ ( 256 ) = 8, because 2^8=256

etc.

 

Common bases:

ln(x) = log_e(x), base is e

log(x) = log₁₀(x), base is 10

 

In your example, if base is 5, then log₅(125)=3

Edited June 2, 201411 yr by Sensei

Yes a good detail by Molecule shared here. ,<link removed by mod>